The answer is yes, as I now have a bulb that produces 2 flowering stems each year, and I must have had it for at least 4 years.
After flowering, I keep it growing in the house until it is warm enough to take it to an unheated greenhouse where I feed it well till the Autumn, when I withhold water and let it die down. Then bring it back inside and start watering again. My original bulb is now surrounded by many babies.